基于Bessel-Legendre不等式的连续广义时滞系统容许性条件  

Admissibility Condition of Continuous Singular Time-Delay Systems Based on Bessel-Legendre Inequality

作　　者：于姗姗 孙欣[1] YU Shanshan;SUN Xin(College of Mathematics and System Science, Shenyang Normal University, Shenyang 110034, China)

机构地区：[1]沈阳师范大学数学与系统科学学院,辽宁沈阳110034

出　　处：《沈阳大学学报（自然科学版）》2020年第2期173-178,共6页Journal of Shenyang University：Natural Science

基　　金：国家自然科学基金资助项目(61374043);辽宁省教育厅高等学校基本科研项目(LFW201711).

摘　　要：研究了连续广义时滞系统的容许性问题.通过将二次型中的向量增加维数构造了一个新的增广的Lyapunov-Krasovskii泛函.然后对泛函求导,再利用三阶Bessel-Legendre不等式和四阶Bessel-Legendre积分不等式处理求导后的某些积分项,得到了一个以线性矩阵不等式形式给出的连续广义时滞系统容许性条件.其中Bessel-Legendre不等式较其他的一些不等式对积分项的放大程度更小.最后,通过数值算例说明了该方法比现有的方法具有更小的保守性.The admissibility condition of continuous singular time-delay systems is addressed.A new augmented Lyapunov-Krasovskii functional is constructed by augmented dimension of vector in the quadratic form.Derivation on the Lyapunov-Krasovskii function produces some of integral terms which will be dealt with third-order Bessel-Legendre inequality and fourth-order Bessel-Legendre integral inequality.The admissibility condition of continuous singular time-delay systems is obtained in the form of linear matrix inequality.Compared with other inequalities,the enlarged degree of the integral terms is less by Bessel-Legendre inequality.A numerical example is illustrated to show that the proposed method is less conservative than other existing ones.

关 键 词：连续广义时滞系统 容许性 LYAPUNOV-KRASOVSKII泛函 Bessel-Legendre不等式 线性矩阵不等式 

分 类 号：O231[理学—运筹学与控制论]